Factor \( x^{3}+5 x^{2}-10 x-50 \) None of these \( \left(x^{2}-10\right)(x+5)^{2} \) \( x^{2}(x+5)-10(x+5) \) \( \left(x^{2}-10\right)(x+5) \)

To factor the polynomial \( x^{3}+5 x^{2}-10 x-50 \), we can start by looking for possible rational roots using the Rational Root Theorem. Testing \( x = -5 \), we find that it satisfies the equation. Once we factor \( x + 5 \) out, we can do synthetic division which leads us to \( x^2 - 10 \) as the other factor. Thus, the complete factorization of the polynomial is \( (x + 5)(x^2 - 10) \). Exploring the roots of \( x^2 - 10 \), we find that it further breaks down to \( (x + 5)(x - \sqrt{10})(x + \sqrt{10}) \), allowing us to express all possible values that satisfy the equation. This shows how effectively polynomials can reveal their hidden factors, leading to insights about their behavior.